Threefold Symmetry Detection in Hexagonal Images Based on Finite Eisenstein Fields

被引：1

作者：

Karkishchenko, Alexander ^{[1
]}

Mnukhin, Valeriy ^{[1
]}

机构：

[1] Southern Fed Univ, 105-42 Bolshaya Sadovaya, Rostov Na Donu 344006, Russia

来源：

ANALYSIS OF IMAGES, SOCIAL NETWORKS AND TEXTS, AIST 2016 | 2017年 / 661卷

基金：

俄罗斯基础研究基金会;

关键词：

Image analysis; Threefold symmetry; Hexagonal image; Eisenstein numbers; Finite fields; Log-polar coordinates; Polar representation; SHAPE;

D O I：

10.1007/978-3-319-52920-2_26

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper considers an algebraic method for symmetry analysis of hexagonally sampled images, based on the interpretation of such images as functions on "Eisenstein fields". These are finite fields GF(p(2)) of special characteristics p = 12k + 5, where k > 0 is an integer. Some properties of such fields are studied; in particular, it is shown that its elements may be considered as "discrete Eisenstein numbers" and are in natural correspondence with hexagons in a (p x p)-diamond-shaped fragment of a regular plane tiling. The concept of logarithm in Eisenstein fields is introduced and used to define a "log-polar"-representation of hexagonal images. Next, an algorithm for threefold symmetry detection in gray-level images is proposed.

引用

页码：281 / 292

页数：12

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